Answer:
The 10th term of the geometric sequence is 13,122.
Step-by-step explanation:
*Assuming that we're going to find the 10th term. If you're going to find the 100th term, it will be impossible. (Just comment if you're really looking for the 100th term, so I can edit my answer and solve it as much as I can.)
Given: [tex]a_1=\frac{2}{3}[/tex], [tex]r=3[/tex], [tex]n=10[/tex]
Find: [tex]a_{10}=?[/tex]
Formula: [tex]a_n=a_1r^{n-1}[/tex]
Solution:
[tex]a_n=a_1r^{n-1}\\a_{10}=(\frac{2}{3})(3)^{10-1}\\a_{10}=(\frac{2}{3})(3)^{9}\\a_{10}=(\frac{2}{3})(19,683)\\a_{10}=(2)(6,561)\\\boxed{a_{10}=13,122}[/tex]
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